t (in millimeters). Foam height is approximately normally distributed an lard deviation of 20 mm. The company wishes to test Ho: u = 175mm versus nm using the test results of n=10 samples Find the type I error probability if the critical region is > 185 The number of samples is now increased to 16. Where would the boundar critical region be placed if the type I error probability were to remain equa value that it took on when n= 10? Using n = 16 and the new critical region determined in (b), find the type

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1. A consumer products company is formulating a new shamp00 and is interested in foam
height (in millimeters). Foam height is approximately normally distributed and has a
standard deviation of 20 mm. The company wishes to test Ho: u = 175mm versus H,:µ >
175 mm using the test results of n= 10 samples
a. Find the type I error probability if the critical region is > 185
b. The number of samples is now increased to 16. Where would the boundary of the
critical region be placed if the type I error probability were to remain equal to the
value that it took on when n= 10?
C. Using n=
16 and the new critical region determined in (b), find the type II error
probability if the true mean foam height is 195 millimeters.
Transcribed Image Text:1. A consumer products company is formulating a new shamp00 and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 mm. The company wishes to test Ho: u = 175mm versus H,:µ > 175 mm using the test results of n= 10 samples a. Find the type I error probability if the critical region is > 185 b. The number of samples is now increased to 16. Where would the boundary of the critical region be placed if the type I error probability were to remain equal to the value that it took on when n= 10? C. Using n= 16 and the new critical region determined in (b), find the type II error probability if the true mean foam height is 195 millimeters.
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